Smooth and weak synthesis of the anti-diagonal in Fourier algebras of Lie groups
| dc.creator | Park, B. Doug | |
| dc.creator | Samei, Ebrahim | |
| dc.date | 2008-09-16 | |
| dc.date.accessioned | 2026-07-07T10:03:26Z | |
| dc.date.available | 2026-07-07T10:03:26Z | |
| dc.description | Let $G$ be a Lie group of dimension $n$, and let $A(G)$ be the Fourier algebra of $G$. We show that the anti-diagonal $\checkΔ_G=\{(g,g^{-1})\in G\times G \mid g\in G\}$ is both a set of local smooth synthesis and a set of local weak synthesis of degree at most $[\frac{n}{2}]+1$ for $A(G\times G)$. We achieve this by using the concept of the cone property in \cite{ludwig-turowska}. For compact $G$, we give an alternative approach to demonstrate the preceding results by applying the ideas developed in \cite{forrest-samei-spronk}. We also present similar results for sets of the form $HK$, where both $H$ and $K$ are subgroups of $G\times G\times G\times G$ of diagonal forms. Our results very much depend on both the geometric and the algebraic structure of these sets. | |
| dc.identifier | https://arxiv.org/abs/0809.2806 | |
| dc.identifier | http://arxiv.org/abs/0809.2806 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169291 | |
| dc.subject | Functional Analysis | |
| dc.subject | Group Theory | |
| dc.subject | 43A30, 43A45 | |
| dc.title | Smooth and weak synthesis of the anti-diagonal in Fourier algebras of Lie groups | |
| dc.type | text |